| Description |
1 online resource |
| Series |
Springer Proceedings in Mathematics and Statistics ; v. 409 |
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Springer proceedings in mathematics & statistics ; v.409.
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| Contents |
Intro -- Preface -- Contents -- Classification of Exceptional Complements: Elliptic Curve Case -- 1 Introduction -- 1.1 The Dual Graph of a Configuration -- 1.2 Types of Singularities on C -- 2 Elliptic Curve Case -- 2.1 Reduction to mathbbF2 -- 2.2 The Search for Exceptions -- References -- Cylinders in Del Pezzo Surfaces of Degree Two -- 1 Introduction -- 2 Del Pezzo Surfaces with Singularities of Type A1 -- 3 Smooth Del Pezzo Surfaces -- 3.1 P is an Intersection Point of Two (-1)-Curves -- 3.2 P is Not an Intersection Point of Two (-1)-Curves -- References |
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Finiteness of Real Structures on KLT Calabi-Yau Regular Smooth Pairs of Dimension 2 -- 1 Introduction -- 2 Preliminaries: Geometric Actions on CAT(0) Spaces -- 3 Finiteness Theorem -- 4 Two Examples -- 5 Appendix -- References -- Anticanonical Volumes of Fano 4-Folds -- 1 Introduction -- 2 Proof of Results -- References -- Constant Scalar Curvature Sasaki Metrics and Projective Bundles -- 1 The Projective Bundles -- 2 The Orbifold Boothby-Wang Construction -- 3 The Topology of the Orbifolds -- 3.1 The Orbifold Cohomology Groups -- 3.2 The Cohomology of the Branched Covers -- 3.3 The Regular Case |
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3.4 The General Case -- Branched Covers -- 3.5 When M7 is an S3w-Join -- 4 Admissible Projective Bundles -- 4.1 Orbifolds -- 4.2 Connection with S3w-Joins -- 4.3 Connection with Yamazaki's Fiber Joins -- 4.4 Ricci Solitons and Kähler-Einstein -- 4.5 Extremal and CSC Kähler Metrics -- 4.6 Weighted Extremal Metrics -- References -- Toric Sarkisov Links of Toric Fano Varieties -- 1 Introduction -- 2 The Context -- 2.1 Overview of the Sarkisov Program -- 2.2 Hard Fano Varieties from Easy Ones -- 2.3 The Midpoints of Sarkisov Links -- 3 Operations on a Simplicial Fan -- 4 Extending Prokhorov's Web |
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4.1 Links from a Smooth Point -- 4.2 Links from the Eighth Toric Mori-Fano 3-Fold -- 4.3 Links from 1-Dimensional Centres -- 4.4 Bounding Links from a Smooth Centre -- 4.5 Higher Rank Fano 3-Folds, Links and Relations -- 5 The Web of 4-Dimensional Toric Sarkisov Links -- 5.1 Blowups of mathbbP(1,2,3,4,5) -- 5.2 Links Between Fake Weighted Projective Spaces -- 5.3 Blowups of mathbbP4 -- 6 Further Related Problems -- 6.1 High-Discrepancy Blowups -- 6.2 Non-terminal Singularities -- 6.3 Running the Sarkisov Program on Toric n-Folds -- 6.4 Higher Picard Rank |
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6.5 Fano 3-Folds and 4-Folds More Generally -- References -- Du Val Singularities -- 1 Introduction -- 2 Finite Subgroups of SL2(mathbbC) -- 3 Description of Du Val Singularities -- 4 A1-Singularity -- 5 E6-Singularity -- 6 Two-Dimensional McKay Correspondence -- References -- K-Polystability of Two Smooth Fano Threefolds -- 1 Introduction -- 2 Smooth Divisor in mathbbP1timesmathbbP1timesmathbbP2 of Degree (1,1,1) -- 3 Blow up of a Complete Intersection of Two Quadrics in a Conic -- References -- A Note on Families of K-Semistable Log-Fano Pairs -- 1 Introduction |
| Summary |
This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: existence of KhlerEinstein metrics on Fano varieties degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous BorisovAlexeevBorisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) TianYauDonaldson Conjecture on the existence of KhlerEinstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Khler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the MoscowShanghaiPohang conferences, while the others helped to expand the research breadth of the volumethe diversity of their contributions reflects the vitality of modern Algebraic Geometry |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed June 5, 2023) |
| Subject |
Geometry, Algebraic -- Congresses
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Geometry, Algebraic
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| Genre/Form |
Electronic books
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proceedings (reports)
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Conference papers and proceedings
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Conference papers and proceedings.
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Actes de congrès.
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| Form |
Electronic book
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| Author |
Cheltsov, Ivan, 1973-
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Chen, Xiuxiong.
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Katzarkov, Ludmil, 1961-
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Park, Jihun, 1970-
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Birational Geometry, Kähler-Einstein Metrics and Degenerations (Conference) (2019 : Moscow, Russia)
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Birational Geometry, Kähler-Einstein Metrics and Degenerations (Conference) (2019 : Shanghai, China)
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Birational Geometry, Kähler-Einstein Metrics and Degenerations (Conference) (2019 : P'ohang-si, Korea)
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| ISBN |
9783031178597 |
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3031178599 |
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